On Wed, 15 Mar 2000, Ralf Sigmund (privat) wrote:
> has anybody an idea, whether the following sentence should be correct?
>
> 'non-overlapping 84% bivariate confidence regions approximate
> statistically significant differences with p < 0.05. Two-sided test.'
I don't recall having seen a reply to this question.
About the bivariate case I am not certain. For the univariate case, with
two independent groups of about the same size, it is roughly correct, if
the confidence regions are the usual symmetrical intervals. Analysis:
For convenience assume equal variances in the two groups. Then the means
differ (p < 0.05) if the distance between them is > 2 standard errors of
the difference (i.e., if t > 2) approximately. For equal sample sizes,
the standard error of the difference = sqrt(2) times the std. error of
the mean; difference between means then > 2.8 std. errors of the mean.
Half that difference = 1.4 std. errors. 84% confidence interval is
(mean +/- 1.4 std. errors); so non-overlapping confidence intervals
would show that the means were at least 1.4 + 1.4 = 2.8 std. errors
apart, hence significantly different (p < 0.05).
It is plausible that a similar relationship holds in the bivariate case.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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